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Is this almost always the case?
Yes. For two reasons. Wider bars move your arms out making the reach effectively longer. Also wider bars make the steering slower. Shorter stem counteracts both of these effects to some degree.
Yes
Also , when negotiating tight turns your outer hand goes further forward.
Yes, [i]almost[/i] always the case.
No, not [i]always[/i] the case as you have to factor in bar sweep. Wider bars *tend* to have more sweep to be more comfortable for hands/ wrists.
Even if two different bars have the same stated sweep they may place your hands in a different position relative to the saddle since the sweep can originate closer or further away from the stem and the two bars actually be quite different. You may or may not notice 🙂
Does that help? 🙂